Montufar et al. [1]} investigate FCNNs with two types of piecewise linear activation functions: ReLU [2]} and Maxout [3]}. They prove that, under certain parameter settings, the model expressive capacity of a ReLU network \(\mathcal {N}\) , which is represented by the maximum number of linear regions and denoted by \(MEC(\mathcal {N})\) , is bounded by
\(MEC(\mathcal {N}) \ge (\prod _{i=1}^{l-1}\lfloor \frac{m_i}{m_0}\rfloor ^{m_0})\sum _{j=0}^{m_0}\tbinom{m_l}{j}\) 
